The sum of the first n positive odd integers = Check all the correct answer/s. Σ I T Σ(2x + 1) 2=1 12 Σ(22 – 1) 2=1 Σ(2n – 1) 2=1 8+2

Q: Using the Laplace transform, solve the IVP. y₁(t) = Y₂(t) = y₁ = 5y₁ - 4y2 - 9t² + 2t, y₂ = 10y₁ -…

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Q: • Find Laplace transform of the function Shown below:- 122

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Q: Which option, if any, would allow you to repay a loan in less time? decrease the regular payment…

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Q: Prove that sin²x x cos²x = csc²x-cot²x 4csc²2x

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Q: Prove that sin²x x cos²x = csc²x-cot²x 4csc²2x

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Q: Evaluate the iterated integral [² [² 2e3² dy dx by changing the order of integration.

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Q: Find the solution of the initial-value problem y" - 6y" +16y'-96y = sec 4t, y(0) = 2, y'(0) = -1,…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: Solve for y esec(4y²−6y+14) = 3x + 1

A: If p=sec q, then it can be written that q=2πn+sec-1π and q=2πn-sec-1π, where n∈Z. Using the…

Q: Example 3: Find the parametric and symmetric equations of the line passing through the point (-3, 5,…

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Q: Having chosen primes p and q, and suitable integers d and e, what is the public-key of our RSA…

A: There are primes p and q and integers d and e, the public-key of RSA cipher is: n,e=pq, e

Q: Question 1 of 14, Step 1 When a factory operates from 6 AM to 6 PM, its total fuel consumption…

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Q: Yn+2 -6yn+1 + 8y = 3n²+2-5.3n Solve the following using Z-Transform, when y(0)=0 and y(1)=1.

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Q: 2π The graph below shows the angle A = 3 A = 2π/3 Find the exact value (no rounding) of sine. 2T sin…

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Q: Suppose T is a linear transformation such that [5] 1, T A 5 -1 = 1, T 3 T2 = -6 3 5 2 Find A such…

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Q: Example 3: Find the parametric and symmetric of the line passing through the point (-3, 5, 4) and…

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Q: Solve the following x²-x²-√√2x lime-21 x²-11x+18

A: Use L' Hospital Rule to evaluate the required limit as in next step.

Q: Consider the initial value problem of a system of linear differential equations x' = Ax+eAt "A], =…

A: The Given Initial value problem is: x'=Ax+eAt01 , x(0)=10, Where A is 2×2 Constant matrix. Let…

Q: Prove that sin²x x cos²x = csc²x-cot²x 4csc²2x

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Q: 6. If k is constant, which of the following equations expresses an inverse variation? C.k= =kn B. x…

A: If p is directly varies as q, then it can be written that p∝q and if If p is inversely varies as q,…

Q: I will invest Nu. 500 per quarter for my retirement at 7.3% compounding quarterly for 32 years. I…

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Q: Q5:A- Show that the boundary-value problem has a unique solution: ý=ýcosx + 2xy, 0≤x≤, y(0) = -0.3,…

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Q: Find a general solution to the differential equation. y" -6y' +9y=t4 e 3t The general solution is…

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Q: Question 5 i) Consider the double integral I = integral 1 = ₁²₁₁ e²² dx dy. y/3 Draw the region of…

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Q: Solve the following x³-x²-√2x limx→2²-11x+18

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Q: 2. A vector # = (a,b,c) has a direction angle of 45° with the positive x-axis and a direction angle…

A: Here a vector r→=a,b,c has a direction angle of 45 with the positive x-axis and a direction of 130…

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A: We have to find volume of solid formed by revolving the curve around y-axis.

Q: er, explicit ODE

A: Note:-  For this problem, I'll provide you definition and example of first order explicit ode and…

Q: Consider the equation -u" + qu 0 and suppose qo ≤ = q(x) ≤ 9₁ < 0. Show that for two consecutive…

A: The solution is hand written as requested:

Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² = 9(x² -…

A: Please see the attachment

Q: b) Consider the following LP problem. Minimize z = 2x₁ + x₂ Subject to 3x₁ + x₂ ≥ 3 4x₁ + 3x₂ ≥6 x₁…

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Q: 11. Consider the function defined by f(x) = e-x². i. ii. iii. Using the Maclaurin series expansion…

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Q: Example 8: Find the point where the line x = 1 + t, y = 2t, and z= -3t intersects the plane…

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Q: sin² x x cos²x csc²x-cot²x 4csc²2x

A: This is the question from other math, finite math and counting and identity.

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Q: 1/ For any. topological space (X, T), if T has only three elements then (X, T) is connected.

A: For any topological space  (X, T) if T has only three elements then  (X, T) is connected

Q: Find the value of b for which the differential equation (ye¹0xy + x) dx + (bxe¹0xy) dy = 0 is exact,…

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Q: 5. Let C be the curve of intersection of the hyperbolic paraboloid z=x² - y² and the cylinder x² +…

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A: A part of the whole thing is known as fraction. We can write a fraction in the form of ab, where a…

Q: Solve the following x²-x²-√√2x lime-21 x²-11x+18

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Q: (b) Compute using polar coordinates quadrant common between circle x² + y² = 2x and circle x² + y² =…

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Q: calculator?

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Q: 2 A sales representative's orders for May were 16% less than her April orders, 3 which amounted to…

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Q: Adam has $450. He spends $210 on food. Later he divides all the money into four parts out of which…

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Q: ● √3x dy dx √x² + y² So So

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Q: - Using prove M the E - f ? f(x) continuous 8 definition of continuity R > R that is defined by 3x +…

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Q: Solve for y esec(4y²-6y+14) = 3x + 1

A: If p=sec q, then it can be written that q=2πn+sec-1π and q=2πn-sec-1π, where n∈Z. The roots of the…